Mass Diffusing Rate through Hollow Cylinder with Solid Boundary Calculator

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Molar Diffusion

Basics of HMT

Conduction

Convection

Convective Mass Transfer

✖Diffusion Coefficient is the magnitude of the molar flux through a surface per unit concentration gradient out-of-plane.ⓘ Diffusion Coefficient [D_ab]			+10% -10%
✖Length of Cylinder is the vertical height of the Cylinder.ⓘ Length of Cylinder [l]			+10% -10%
✖Mass Concentration of Component A in Mixture 1 is the concentration of component A per unit volume in mixture 1.ⓘ Mass Concentration of Component A in Mixture 1 [ρ_a1]			+10% -10%
✖The Mass Concentration of component A in Mixture 2 is the concentration of component A per unit volume in mixture 2.ⓘ Mass Concentration of Component A in Mixture 2 [ρ_a2]			+10% -10%
✖The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder.ⓘ Outer Radius of Cylinder [r₂]			+10% -10%
✖The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.ⓘ Inner Radius of Cylinder [r₁]			+10% -10%

✖Mass Diffusing Rate is the proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species.ⓘ Mass Diffusing Rate through Hollow Cylinder with Solid Boundary [m_a]

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Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Formula

`"m"_{"a"} = (2*pi*"D"_{"ab"}*"l"*("ρ"_{"a1"}-"ρ"_{"a2"}))/ln("r"_{"2"}/"r"_{"1"})`

Example

`"9333.737kg/s"=(2*pi*"0.8m²/s"*"102m"*("40kg/m³"-"20kg/m³"))/ln("7.5m"/"2.5m")`

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Mass Diffusing Rate through Hollow Cylinder with Solid Boundary Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Diffusing Rate = (2*pi*Diffusion Coefficient*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder)
m_a = (2*pi*D_ab*l*(ρ_a1-ρ_a2))/ln(r₂/r₁)
This formula uses 1 Constants, 1 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Mass Diffusing Rate - (Measured in Kilogram per Second) - Mass Diffusing Rate is the proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species.
Diffusion Coefficient - (Measured in Square Meter Per Second) - Diffusion Coefficient is the magnitude of the molar flux through a surface per unit concentration gradient out-of-plane.
Length of Cylinder - (Measured in Meter) - Length of Cylinder is the vertical height of the Cylinder.
Mass Concentration of Component A in Mixture 1 - (Measured in Kilogram per Cubic Meter) - Mass Concentration of Component A in Mixture 1 is the concentration of component A per unit volume in mixture 1.
Mass Concentration of Component A in Mixture 2 - (Measured in Kilogram per Cubic Meter) - The Mass Concentration of component A in Mixture 2 is the concentration of component A per unit volume in mixture 2.
Outer Radius of Cylinder - (Measured in Meter) - The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder.
Inner Radius of Cylinder - (Measured in Meter) - The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.

STEP 1: Convert Input(s) to Base Unit

Diffusion Coefficient: 0.8 Square Meter Per Second --> 0.8 Square Meter Per Second No Conversion Required
Length of Cylinder: 102 Meter --> 102 Meter No Conversion Required
Mass Concentration of Component A in Mixture 1: 40 Kilogram per Cubic Meter --> 40 Kilogram per Cubic Meter No Conversion Required
Mass Concentration of Component A in Mixture 2: 20 Kilogram per Cubic Meter --> 20 Kilogram per Cubic Meter No Conversion Required
Outer Radius of Cylinder: 7.5 Meter --> 7.5 Meter No Conversion Required
Inner Radius of Cylinder: 2.5 Meter --> 2.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m_a = (2*pi*D_ab*l*(ρ_a1-ρ_a2))/ln(r₂/r₁) --> (2*pi*0.8*102*(40-20))/ln(7.5/2.5)

Evaluating ... ...

m_a = 9333.73723112873

STEP 3: Convert Result to Output's Unit

9333.73723112873 Kilogram per Second --> No Conversion Required

FINAL ANSWER

9333.73723112873 ≈ 9333.737 Kilogram per Second <-- Mass Diffusing Rate

(Calculation completed in 00.020 seconds)

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Home » Physics » Heat and Mass Transfer » Molar Diffusion » Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

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Created by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< 17 Molar Diffusion Calculators

Molar Flux of Diffusing Component A through Non-Diffusing B based on Partial Pressure of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/([R]*Temperature of Gas*Film Thickness))*ln((Total Pressure of Gas-Partial Pressure of Component A in 2)/(Total Pressure of Gas-Partial Pressure of Component A in 1))

Molar Flux of Diffusing Component A through Non-Diffusing B based on Log Mean Partial Pressure

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/([R]*Temperature of Gas*Film Thickness))*((Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)/Log Mean Partial Pressure of B)

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Go Mass Diffusing Rate = (2*pi*Diffusion Coefficient*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Partial Pressure of B

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/([R]*Temperature of Gas*Film Thickness))*ln(Partial Pressure of Component B in 2/Partial Pressure of Component B in 1)

Mass Diffusing Rate through Solid Boundary Sphere

Go Mass Diffusing Rate = (4*pi*Inner Radius*Outer Radius*Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/(Outer Radius-Inner Radius)

Molar Flux of Diffusing Component A for Equimolar Diffusion with B based on Mole Fraction of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/([R]*Temperature of Gas*Film Thickness))*(Mole Fraction of Component A in 1-Mole Fraction of Component A in 2)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of A and LMPP

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*(Total Pressure of Gas^2))/(Film Thickness))*((Mole Fraction of Component A in 1-Mole Fraction of Component A in 2)/Log Mean Partial Pressure of B)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Concentration of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/(Film Thickness))*((Concentration of Component A in 1-Concentration of Component A in 2)/Log Mean Partial Pressure of B)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of A and LMMF

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/(Film Thickness))*((Mole Fraction of Component A in 1-Mole Fraction of Component A in 2)/Log Mean Mole Fraction of B)

Logarithmic Mean Partial Pressure Difference

Go Logarithmic Mean Partial Pressure Difference = (Partial Pressure of Component B in Mixture 2-Partial Pressure of Component B in Mixture 1)/(ln(Partial Pressure of Component B in Mixture 2/Partial Pressure of Component B in Mixture 1))

Logarithmic Mean of Concentration Difference

Go Logarithmic Mean of Concentration Difference = (Concentration of Component B in Mixture 2-Concentration of Component B in Mixture 1)/ln(Concentration of Component B in Mixture 2/Concentration of Component B in Mixture 1)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/(Film Thickness))*ln((1-Mole Fraction of Component A in 2)/(1-Mole Fraction of Component A in 1))

Molar Flux of Diffusing Component A for Equimolar Diffusion with B based on Partial Pressure of A

Go Molar Flux of Diffusing Component A = (Diffusion Coefficient (DAB)/([R]*Temperature of Gas*Film Thickness))*(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of B

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/(Film Thickness))*ln(Mole Fraction of Component B in 2/Mole Fraction of Component B in 1)

Mass Diffusing Rate through Solid Boundary Plate

Go Mass Diffusing Rate = (Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)*Area of Solid Boundary Plate)/Thickness of Solid Plate

Convective Mass Transfer Coefficient

Go Convective Mass Transfer Coefficient = Mass Flux of Diffusion Component A/(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)

Total Concentration

Go Total Concentration = Concentration of A+Concentration of B

< 3 Mass Diffusing Rate Calculators

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Mass Diffusing Rate through Solid Boundary Sphere

Mass Diffusing Rate through Solid Boundary Plate

Go Mass Diffusing Rate = (Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)*Area of Solid Boundary Plate)/Thickness of Solid Plate

< 16 Important Formulas in Diffusion Calculators

Diffusivity by Stefan Tube Method

Go Diffusion Coefficient (DAB) = ([R]*Temperature of Gas*Log Mean Partial Pressure of B*Density of Liquid*(Height of Column 1^2-Height of Column 2^2))/(2*Total Pressure of Gas*Molecular Weight A*(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)*Diffusion Time)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Partial Pressure of A

Diffusivity by Twin Bulb Method

Go Diffusion Coefficient (DAB) = ((Length of Tube/(Inner Cross Section Area*Diffusion Time))*(ln(Total Pressure of Gas/(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2))))/((1/Volume of Gas 1)+(1/Volume of Gas 2))

Molar Flux of Diffusing Component A through Non-Diffusing B based on Log Mean Partial Pressure

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Mass Diffusing Rate through Solid Boundary Sphere

Fuller-Schettler-Giddings for Binary Gas Phase Diffusivity

Go Diffusion Coefficient (DAB) = ((1.0133*(10^(-7))*(Temperature of Gas^1.75))/(Total Pressure of Gas*(((Total Atomic Diffusion Volume A^(1/3))+(Total Atomic Diffusion Volume B^(1/3)))^2)))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2))

Molar Flux of Diffusing Component A for Equimolar Diffusion with B based on Mole Fraction of A

Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of A and LMPP

Molar Flux of Diffusing Component A through Non-Diffusing B based on Concentration of A

Chapman Enskog Equation for Gas Phase Diffusivity

Go Diffusion Coefficient (DAB) = (1.858*(10^(-7))*(Temperature of Gas^(3/2))*(((1/Molecular Weight A)+(1/Molecular Weight B))^(1/2)))/(Total Pressure of Gas*Characteristic Length Parameter^2*Collision Integral)

Molar Flux of Diffusing Component A through Non-Diffusing B based on Mole Fractions of A

Go Molar Flux of Diffusing Component A = ((Diffusion Coefficient (DAB)*Total Pressure of Gas)/(Film Thickness))*ln((1-Mole Fraction of Component A in 2)/(1-Mole Fraction of Component A in 1))

Molar Flux of Diffusing Component A for Equimolar Diffusion with B based on Partial Pressure of A

Go Molar Flux of Diffusing Component A = (Diffusion Coefficient (DAB)/([R]*Temperature of Gas*Film Thickness))*(Partial Pressure of Component A in 1-Partial Pressure of Component A in 2)

Mass Diffusing Rate through Solid Boundary Plate

Go Mass Diffusing Rate = (Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)*Area of Solid Boundary Plate)/Thickness of Solid Plate

Wilke Chang Equation for Liquid Phase Diffusivity

Go Diffusion Coefficient (DAB) = (1.173*(10^(-16))*((Association Factor*Molecular Weight B)^(1/2))*Temperature of Gas)/(Dynamic Viscosity of Liquid*((Molar Volume of Liquid/1000)^0.6))

Molar Flux of Diffusing Component A for Equimolar Diffusion with B based on Concentration of A

Go Molar Flux of Diffusing Component A = (Diffusion Coefficient (DAB)/(Film Thickness))*(Concentration of Component A in 1-Concentration of Component A in 2)

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary Formula

What is Molar diffusion?

Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random motion of the molecules. The result of diffusion is a gradual mixing of material such that the distribution of molecules is uniform. Since the molecules are still in motion, but an equilibrium has been established, the end result of molecular diffusion is called a "dynamic equilibrium".

How to Calculate Mass Diffusing Rate through Hollow Cylinder with Solid Boundary?

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary calculator uses Mass Diffusing Rate = (2*pi*Diffusion Coefficient*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder) to calculate the Mass Diffusing Rate, Mass Diffusing Rate through Hollow Cylinder with Solid Boundary is defined as amount of particles diffusing through Hollow Cylinder with Solid Boundary per unit time. Mass Diffusing Rate is denoted by m_a symbol.

How to calculate Mass Diffusing Rate through Hollow Cylinder with Solid Boundary using this online calculator? To use this online calculator for Mass Diffusing Rate through Hollow Cylinder with Solid Boundary, enter Diffusion Coefficient (D_ab), Length of Cylinder (l), Mass Concentration of Component A in Mixture 1 (ρ_a1), Mass Concentration of Component A in Mixture 2 (ρ_a2), Outer Radius of Cylinder (r₂) & Inner Radius of Cylinder (r₁) and hit the calculate button. Here is how the Mass Diffusing Rate through Hollow Cylinder with Solid Boundary calculation can be explained with given input values -> 9333.737 = (2*pi*0.8*102*(40-20))/ln(7.5/2.5).

FAQ

What is Mass Diffusing Rate through Hollow Cylinder with Solid Boundary?

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary is defined as amount of particles diffusing through Hollow Cylinder with Solid Boundary per unit time and is represented as m_a = (2*pi*D_ab*l*(ρ_a1-ρ_a2))/ln(r₂/r₁) or Mass Diffusing Rate = (2*pi*Diffusion Coefficient*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder). Diffusion Coefficient is the magnitude of the molar flux through a surface per unit concentration gradient out-of-plane, Length of Cylinder is the vertical height of the Cylinder, Mass Concentration of Component A in Mixture 1 is the concentration of component A per unit volume in mixture 1, The Mass Concentration of component A in Mixture 2 is the concentration of component A per unit volume in mixture 2, The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder & The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.

How to calculate Mass Diffusing Rate through Hollow Cylinder with Solid Boundary?

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary is defined as amount of particles diffusing through Hollow Cylinder with Solid Boundary per unit time is calculated using Mass Diffusing Rate = (2*pi*Diffusion Coefficient*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder). To calculate Mass Diffusing Rate through Hollow Cylinder with Solid Boundary, you need Diffusion Coefficient (D_ab), Length of Cylinder (l), Mass Concentration of Component A in Mixture 1 (ρ_a1), Mass Concentration of Component A in Mixture 2 (ρ_a2), Outer Radius of Cylinder (r₂) & Inner Radius of Cylinder (r₁). With our tool, you need to enter the respective value for Diffusion Coefficient, Length of Cylinder, Mass Concentration of Component A in Mixture 1, Mass Concentration of Component A in Mixture 2, Outer Radius of Cylinder & Inner Radius of Cylinder and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mass Diffusing Rate?

In this formula, Mass Diffusing Rate uses Diffusion Coefficient, Length of Cylinder, Mass Concentration of Component A in Mixture 1, Mass Concentration of Component A in Mixture 2, Outer Radius of Cylinder & Inner Radius of Cylinder. We can use 6 other way(s) to calculate the same, which is/are as follows -

Mass Diffusing Rate = (4*pi*Inner Radius*Outer Radius*Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/(Outer Radius-Inner Radius)
Mass Diffusing Rate = (Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)*Area of Solid Boundary Plate)/Thickness of Solid Plate
Mass Diffusing Rate = (Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)*Area of Solid Boundary Plate)/Thickness of Solid Plate
Mass Diffusing Rate = (4*pi*Inner Radius*Outer Radius*Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/(Outer Radius-Inner Radius)
Mass Diffusing Rate = (Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)*Area of Solid Boundary Plate)/Thickness of Solid Plate
Mass Diffusing Rate = (4*pi*Inner Radius*Outer Radius*Diffusion Coefficient*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/(Outer Radius-Inner Radius)

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